ARITHMETIC THE SECOND
From these three men Dedekind got a thorough, grounding in
the calculus, the elements of the higher arithmetic, least
squares, higher geodesy, and experimental physics.
In later life Dedekind regretted that the mathematical in-
struction available during his student years at Gottingen, while
adequate for the rather low requirements for a state teacher's
certificate, was inconsiderable as a preparation for a mathe-
matical career. Subjects of living interest were not touched
upon, and Dedekind had to spend two years of hard labour
after taking his degree to get up by himself elliptic functions,
modern geometry, higher algebra, and mathematical physics -
all of which at the time were being brilliantly expounded at
Berlin by Jacobi, Steiner, and Dirichlet. In 1852 Dedekind got
Ms doctor's degree (at the age of twenty-one) from Gauss for a
short dissertation on Eulerian integrals. There is no need to
explain what this was: the dissertation was a useful, indepen-
dent piece of work, but it betrayed no such genius as is evident
on every page of Dedekind's later works. Gauss' verdict on the
dissertation will be of interest: 'The memoir prepared by Herr
Dedekind is concerned with a research in the integral calculus,
which is by no means commonplace. The author evinces not
only a very good knowledge of the relevant field, but also such
an independence as augurs favourably for his future achieve-
ment. As a test essay for admission to the examination I find
the memoir completely satisfying.* Gauss evidently saw more
in the dissertation than some later critics have detected;
possibly his close contact with the young author enabled him
to read between the lines. However, the report, even as it
stands, is more or less the usual perfunctory politeness custo-
mary in accepting a passable dissertation, and we do not know
whether Gauss really foresaw Dedekind's penetrating origin-
ality.
In 1854 Dedekind was appointed lecturer (Privatdozent) at
Gottingen, a position which he held for four years. On the death
of Gauss in 1855 Dirichlet moved from Berlin to Gottingen.
For the remaining three years of his stay at Gottingen, Dede-
kind attended Dirichlet's most important lectures. Later he was
to edit Dirichlet's famous treatise on the theory of numbers and
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